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Graph of f Is a Subset Of …
publish date: 2026/05/23 18:30:38.326435 UTC
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For a function \(f: A \to B\) with \(A, B \subseteq \mathbb{R}\), the graph of \(f\) is a subset of:
Correct Answer
\(A \times B\)
Explanation
Each point on the graph is an ordered pair \((a, f(a))\) where \(a \in A\) and \(f(a) \in B\). So the graph is a subset of \(A \times B\). It is in general a proper subset of \(A \times B\) — most points in \(A \times B\) are not on the graph. Only for a bijection does the graph "use" each element of both sets exactly once.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012